An Introduction to Formal Logic

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Cambridge University Press, Nov 6, 2003 - Mathematics - 357 pages
3 Reviews
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
 

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Some explanations are drawn out, but this drawn out approach gives Smith the opportunity to repeat himself - thus making the material easier to retain. It may take me longer than other works to cover a subject, but I feel like my ability to recall the material is far better than other Formal Logic book's i've attempted to read. Also, unlike most Formal Logic texts, solutions to the many exercises are provided online.  

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Contents

What is logic?
1
Validity and soundness
9
Patterns of inference
18
The counterexample technique
29
Proofs
36
Validity and arguments
44
Logic formal and informal
51
Three prepositional connectives
53
After prepositional logic
192
Quantifiers
194
QL introduced
202
QL explored
210
More QL translations
219
Introducing QL trees
228
The syntax of QL
242
Qvaluations
250

The syntax of PL
63
The semantics of PL
72
As and Bs Ps and Qs
82
Truth functions
88
Tautologies
101
Tautological entailment
107
Propositional logic
123
PLC and the material conditional
125
More on the material conditional
137
Introducing PL trees
145
Rules for PL trees
157
PLC trees
171
PL trees vindicated
179
Trees and proofs
185
Qvalidity
262
More on QL trees
272
QL trees vindicated
286
Developing predicate logic
294
Extensionality
296
Identity
303
The language QL
309
Descriptions and existence
316
Trees for identity
325
Functions
339
Further reading
348
Index
352
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About the author (2003)

Peter Smith's publications include The Philosophy of Mind (1986) and Explaining Chaos (1998).

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